4.2  Optical depth

At lower temperatures, in the chromosphere-transition region, spectral lines become optically thick. Fortunately, it is possible in a number of cases to check which lines are optically thick, and to what extent (see Del Zanna et al. 2002).

One way is to observe the doublets of the Li-like ions (e.g. Si IV, C IV, N V, and O VI). In the optically thin case, the ratios of the two lines of the doublet should be equal to the ratio of the oscillator strengths, i.e. 2. If opacity effects are present, the ratio would decrease, with the brightest component ²S_1/2 - ²P_3/2 being more affected, having a higher oscillator strength. In this case, the ratio is a direct measure of the ratio of the photon escape probabilities, from which the optical depths of the lines can be obtained.

Another way is to observe lines that originate from a common upper level (a branching ratio). In the optically thin case, the ratios are equal to the ratios of the A-values (Jordan 1967).

Table 1: [from Del Zanna et al. 2002] The line ratios in the STIS and FUSE spectral ranges useful for optical depth estimates. The last two columns indicate the theoretical (optical thin case) and the observed ratio values.

Ion	Terms	Wavelengths (Å)	Th.	Ob.
C II	2P3/2 - 2S1/2 /
	2P1/2 - 2S1/2	1037.020/1036.332	2	1.5
Si II	¢¢	1533.430/1526.706	2	1.2
C III	3P0 - 3P1 /
	3P2 - 3P1	1175.265/1176.372	0.8	1.0
Si III	¢¢	1296.726/1303.323	0.8	0.5
C III	3P2 - 3P2 /
	3P1 - 3P2	1175.713/1174.935	3	1.9
Si III	¢¢	1298.944/1294.543	3	2
Si IV	2S1/2 - 2P3/2 /
	2S1/2 - 2P1/2	1393.755/1402.770	2	1.7
C IV	¢¢	1548.201/1550.772	2	2
N V	¢¢	1238.821/1242.804	2	2
O VI	¢¢	1031.914/1037.615	2	2